Here we go again!. When you ask for help you need to provide
which version of: Windows, Firewall software like Zone Alarm, Anti Spyware, anti viri etc.
The other computer is someone else's PC in the local area.
Check this link for details on how to hide XP if that is the version you are using.
Download Audio files and documents 81 - 84 to study securing Windows XP WiFi connections. And read the supplemental notes too.
As far as the dropped connection it happens with Cable and DSL modems but should not happen on regular basis.
Download IpSwitch's WS ping pack Pro to test your connection. It is free for 30 days so have at it! You can set it to check all TCP/IP parameters and start a series of tests, which can be set to run every 30 minutes for as long as you like. I would let it run when you are not using the PC to monitor the connection over night and during the day when the PC is ideal. This creates a log you can copy/cut/paste and send to tech support. You can measure connection speed, delays, loop time etc.